Precision of Z-coordinate
I think I found the problem.
Look at the diagonal in the picture, I just output the z pass, and get the high frequencies with substracting a blurry pass. Then the power node just reveals the error for the eye.

The effect is only with Blender internal, and not with cycles. There is an error along the edge which is the diagonal of the plane.
Now I'm not sure why it does this, but I think it's probably something like as said above:
&quot;Just an hypothesis, if the errors match the diagonal of the plane: maybe with floating point errors, the rays pass through the plane (on the edge), and then with sampling (I don't know if the z pass has several samples, for anti-aliasing, need to check somewhere) it mixes the good value with the 'inf' value, producing the errors.&quot;
Maybe the devs are aware of the problem, I don't know.
[EDIT]
In addition here is the same pass with cycles:

The z error is not here, AND the z seems to be correctly computed. I mean by this that with blender internal z is the distance between the geometry and the plane which crosses the camera, but in cycles z seems to be the distance between the geometry and the point from which the ray is casted (so on the sensor).
So here with cycles Z depends on Y and X, not only Y.
Also the white borders you see on both images are due to the blur combine with the power node, it's a normal effect.